The recent availability of Non-Manifold Topology (NMT) enables the coexistence of wireframe geometry, surfaces, and solids in a single representation with complete topological resolution. This in turn allows a new approach to boundary evaluation. This new approach merges a set of primitives into a single Boundary REPresentation (B-rep), and selects the desired Boolean results without destroying any B-rep entities. The results of the Boolean operations are displayed by drawing only selected entities. The B-rep resulting from the merge contains a complete description of the input primitives. While traditional algorithms allow incremental addition of primitives, this new approach also allows incremental deletion of primitives from the merged B-rep. Changes in Boolean operators and/or their order of evaluation can be reflected in the B-rep simply by changing the criteria of the selection process. Constructive Solid Geometry (CSG) editing operations can be mirrored in the B-rep incrementally, i.e. without performing complete reevaluation of the B-rep from its constituent primitive definitions. In addition, the domain of boundary evaluation has been extended to include Boolean operations between wireframe geometry, surfaces, and solids. This new approach has been successfully implemented and tested to boundary evaluation. Test results have shown an order of magnitude reduction in the cost associated with reflecting CSG editing operations on existing B-reps, with only minimal additional cost for initial construction. Also shown are examples of Boolean operations between solids, surfaces, and wires